A contact lens consists of front and back surface with the back surface is placed against the cornea of the eye. As a person develops deficiency to accommodate from far to near objects, multifocal contact lens can be used to compensate for the lack of the accommodation. There are simultaneous vision contact lenses which form images from distance and near objects simultaneously at the retina to allowing the person to rely on the image that is in focus and ignore another which is out of focus; and translating contact lens that are designed to move up and down on the cornea to expose lens portions either for far or near viewing.
This invention primarily addresses simultaneous vision contact lenses and more specifically diffractive contact lens where diffraction grating placed on one of the surfaces to form different orders that associate with either far and near foci. Cohen and Freeman are the principal inventors of ophthalmic multifocal diffractive optic and particularly multifocal contact lens that utilizes several diffractive orders to form image from the objects at different distances. The Cohen patents: U.S. Pat. Nos. 4,210,391; 4,338,005; 4,340,283; 4,881,805; 4,995,714; 4,995,715; 5,054,905; 5,056,908; 5,117,306; 5,120,120; 5,121,979; 5,121,980 and 5,144,483. The Freeman patents: U.S. Pat. Nos. 4,637,697; 4,641,934; 4,642,112; 4,655,565, 5,296,881 and 5,748,282 where the U.S. Pat. No. 4,637,697 references to the blaze as well as step-shapes (binary) diffractive surface.
A multifocal diffractive optic may be constructed by blazed shaped grooves that are placed on the back surface of the contact lens or dual zone groove described by Fiola and Pingitzer in the U.S. Pat. No. 6,120,148 that can be placed on the front surface of the lens due to smoother surface transition between the grooves. Regardless of particular multifocal surface grooves configuration, the grooves are structured to direct substantial portions of light between zero order for far and first-order for near foci forming diffractive bifocal optic.
The average pupil size of the eye at normal photopic lighting condition is around 3 mm diameter and increases or dilates to about 6 mm diameter al low light condition called mesopic condition. Size of dilated pupil depends upon the eye and usually reduces with age. Changes in pupil size contribute to imaging quality of the eye—the image quality usually reduces with pupil dilation. In addition to pupil size, the lens movement over the cornea results in lens decentration (radial translation) and tilt (axial rotation), jointly called lens shift, may significantly contribute to the image quality particularly in multifocal optic. Contact lens must move on the cornea for corneal health and this is the reason to use the term lens “shift” instead of “misalignment” in referencing to contact lens movement over the cornea. The contact lens shift magnitudes can be found in paper by G. Young, et al. “Comparative Performance of Disposable Soft Contact Lenses”, Contact Lens and Ant Eye; 1997: 20; pp 13-21. In the majority of conditions the lens shifting over the cornea falls within about 0.6 mm decentration. The corresponding lens axial rotation or tilt due to lens movement over the curved corneal surface is about 4.4° for an average corneal radial shape.
There are overlapping terms such as “Base surface” used for back surface of a contact lens and in conjunction with diffractive surface as a imaginable surface responsible for far focus over which the diffraction grooves are placed. In order to avoid confusion, the term “Base surface” is only applied to the optical surface that incorporates multifocal diffraction zone. Thus, Base surface in this disclosure may be a front surface of the contact lens or back surface of the contact lens. The sides of the contact lens surfaces will be distinguished by referencing to as “front surface” or “back surface”.
Base surface together with the opposite refractive surface of the lens responsible for the direction of zero order diffraction used for far vision. Base surface shape together with the shape of the opposite refractive surface are also responsible for the amount of aberrations at far vision. The diffraction surface may occupy the full optical zone of the contact lens or only portion of the zone. In later case, the shape of the surface outside of the diffraction portion also contributes to a position of far focus and aberrations at far vision. In order to avoid repetition in distinguishing between diffraction zone occupying full lens optical zone or only partial optical zone, the total surface within the lens optical zone that is responsible for far focus position will be referenced to as Base surface. Commonly, the Base surface of the contact lens is of spherical shape.
The final quality of the far image depends upon aberrations of the eye with the contact lens on it. Within some range of aberrations a surface is still considered to be monofocal or single focus surface. In terms of diopters, a range of aberrations that produces foci spread along the optical axis of up to about 0.5 D (about 0.25 mm range) at nominal 3 mm pupil is still considered single focus and the corresponding surface is single focus surface. If the range of aberrations produces foci spread more that about 0.5 D for 3 mm pupil, the corresponding contact lens is called “Aspheric contact lens”. There is historical difference in terms “aspheric” applied to contact lenses and intraocular lenses—“aspheric contact lens” means multifocal contact lens that expends foci along the optical axis beyond normal aberrations of single focus optic; “aspheric intraocular lens” means single focus lens with a surface shaped to reduce the aberrations from the spherical intraocular lens of the same power. In order to avoid confusion, the terms “aspheric” and “aspherization” are not used in this disclosure and more general terms “non-spherical” and “reshaping” are applied instead.
Even in a perfectly centered position of spherical contact lens there is still spherical aberration which might be substantial at large pupil sizes at mesopic condition. The reshaping of one of spherical surfaces of the lens eliminates spherical aberrations occurred in the lens centered position. This can be accomplished by progressively increasing radius for front surface or progressively reducing radius for back surface of the lens. The difference arises because front surface is convex surface, i.e. positive power, and back surface is concave surface, i.e. negative power. Progressively increasing or reducing radius of the surface within the optical zone is characteristic of so called prolate shaped surface.
Nevertheless, the clinical testing indicates that image quality doesn't practically improves with lens surface reshaping that reduces eye spherical aberration (SA) due to additional aberration such as coma resulted with contact lens movement over the corneal surface, see paper by H. H. Dietze and M. J. Cox; “Correcting ocular spherical aberration with soft contact lenses”, J. Opt. Soc. Am. A: 21: 2004, pp 473-485. The paper concluded that “Physiological corneal tilt and/or imperfect lens centration can produce levels of coma-like aberration, reducing the visual benefits of correcting SA with contact lenses using aspheric surfaces”. Note, “aspheric surface” terminology used in the paper referred to custom made monofocal non-spherical surface to eliminate spherical aberration, not a multifocal surface where the corresponding terms commonly used in case of contact lenses. The custom surface in the above paper was ellipsoidal shape surface, i.e. prolate non-spherical shape.
Thus, there is the need for a better solution for optic that would maintain the imaging superiority over the lenses that incorporate spherical surface for far vision either in monofocal or multifocal diffractive lens of the equivalent far power within the range of clinically common contact lens movement over the corneal surface.
In order to explain the invention the following background information is also provided.
It has been a common approach to describe aspheric lens aberrations in terms of wavefront aberrations. Wavefront Error can be represented mathematically as Zernike Polynomial Decomposition W(ρ,θ)=Σan,mZnm(ρ,θ), where Znm(ρ,θ) are Zernike radial polynomials of n-order and m-frequency and an,m are Zernike Coefficients as the measure of wavefront aberrations and commonly called “aberrations”. In this Zernike Polynomial Decomposition, 2nd order aberrations are called Low Order Aberrations (LOA) which includes defocus and astigmatism, and aberrations above 2nd order are called High Order Aberrations (HOA). They include spherical aberration, coma, trefold, etc.
There is certain misconception about wavefront aberrations as applied to ocular imaging because they are mathematical abstraction and do not directly represent light distribution at the retina in a form of spot diagram. Their impact on the image quality can only be measured through their relationship with ray aberrations which directly relate to the light distribution at the retinal image.
The key benefit of wavefront aberrations lies in the ability to assess a relative contribution on the optical quality by different wavefront aberrations. This is because Zernike radial polynomials are normalized orthogonal set of functions and their coefficients which are called “wavefront aberration”, can be easily combined into groups by Root Mean Square (RMS) per formula RMS2=Σ(an,m)2. For instance, one can combine Low Order Aberration into RMSLOA and high order aberrations into RMSHOA in order to assess their relative contributions to the optical quality. Low order wavefront aberrations are related to ray aberrations such as defocus and astigmatism jointly called refractive error which is correctable by conventional optical aids such as glasses, contact lenses and IOLs, but high order aberrations generally are not.
In order to understand a relationship between the aberrations and light distribution at the retina, optically called spot diagram, one has to include ray aberrations. The relationship between wavefront and ray aberrations can be found for instance in James C Wyant, “Basic Wavefront Aberration Theory for Optical Metrology”, Applied Optics and Optical Engineering, Vol. XI, Chapter 1, 1992.
Wavefront error is usually defined at the Entrance Pupil of the optical system as W(x,y), where x, y are pupil Cartesian coordinates. Assuming the wavefront error W(x,y) is relatively small and the angle between the reference and aberrated wavefronts is also small, FIG. 2. This angle αx is called angular aberration of the ray and defined by the first derivative of the wavefront error
      α    x    =                    -                  ∂                      W            ⁡                          (                              x                ,                y                            )                                                  n        ⁢                  ∂          x                      .  The corresponding transverse aberration Tx and longitudinal aberration L of the ray are also defined by the first derivative of the wavefront aberration:
            T      x        =                            R          w                ⁢                  α          x                    =                        -                      R            w                          ⁢                              ∂                          W              ⁡                              (                                  x                  ,                  y                                )                                                          n            ⁢                          ∂              x                                            ;the same for Ty; as transverse ray aberrations along x and y-coordinates at the pupil. The ratio of the longitudinal ray aberration and transverse ray aberration
      L          T      x        ≈            R      w              (              x        -                  T          x                    )        ≈                    R        w            x        ⁢                  ⁢    and    ⁢                  ⁢    L    ≈                    R        w        2            x        ⁢                            ∂                      W            ⁡                          (                              x                ,                y                            )                                                n          ⁢                      ∂            x                              .      It is resulted in the difference between the distances to the aberrated ray focus and perfect ray focus where foci are defined as the points of intersections of these rays with the optical axis.
Thus, wavefront aberrations have abstract mathematical meaning of the coefficients in Zernike Polynomial Decomposition but at certain low enough orders of the wavefront aberrations such defocus, astigmatism, spherical aberration and coma, they correlate per above equations with the ray aberrations under the same names. Ray aberrations have physical meaning of light energy travel and can be geometrically interpreted by light rays distribution at the retina. This allows to describing the invention in geometrical terms which are more perceptible than abstract mathematical terms of wavefront aberrations.
In summary, there are two measures of vision quality: (1) pupil based which are wavefront related such as wavefront aberrations and RMS because wavefront is defined at the pupil plane of the eye, and (2) image plane based such as PSF Point Spread Function), Strehl Ratio and MTF related which are derived from the spot diagram at the image plane, i.e. an image of the point object at the retina. Aberrometry used for measuring eye aberrations directly measures spot diagram and derives all other measures from it.
Pupil based measures are in good correlation with vision quality for 3 mm pupil and smaller because the aberrations are only small fraction of the wavelength. At this condition of the nominal eye is almost diffractive limited system and its Strehl Raito is 0.8 or higher. At this condition there is a linear relationship between Strehl Ratio and (RMS2), i.e. pupil based measure lineally relates to pupil based measure and one can use either one for image quality analysis.
It has been shown that for larger pupils with large aberrations, pupil based measures are in poor correlation with vision quality and image plane based measures are much better to use in these conditions. At very large aberrations, spot diagram size becomes a dominant factor. Thus, it is more appropriate to utilize spot diagram and corresponding ray aberrations for image quality analysis at large pupil and lens misalignment where the aberrations are significant either in monofocal optic and particularly multifocal optic.
The simplest ray aberration to interpret is longitudinal ray aberration as being one-dimensional characteristic as the transverse (tangential) ray aberration is defined by two-dimensional characteristic. For optically centered system, longitudinal ray aberration is also called longitudinal spherical aberration or LSA. One can divide the entrance pupil or lens surface along, say x-meridian, into the regions. Each region can be characterized by its own longitudinal spherical aberration and the total spot diagram can be analyzed as a combination of spot diagrams from the regions. Below we will use ray aberrations and specifically longitudinal ray aberration for describing the invention.